BEM-FEM coupling is desirable for three-dimensional problems involving specific features such as (i) large or unbounded media with linear constitutive properties, (ii) cracks, (iii) critical parts of complex geometry requiring accurate stress analyses. However, for cases with a BEM discretization involving a large number NBEM of degrees of freedom, setting up the BEM contribution to the coupled...

Due to improvements in computational resources, interest has recently increased in using implicit scheme for solving flow equations on 3D unstructured grids. However, most of the implicit schemes produce greater numerical diffusion error than their corresponding explicit schemes. This stems from the fact that in linearizing implicit fluxes, it is conventional to replace the Jacobian matrix in t...

‎the global generalized minimum residual (gl-gmres)‎ ‎method is examined for solving the generalized sylvester matrix equation‎ ‎[sumlimits_{i = 1}^q {a_i } xb_i = c.]‎ ‎some new theoretical results are elaborated for‎ ‎the proposed method by employing the schur complement‎. ‎these results can be exploited to establish new convergence properties‎ ‎of the gl-gmres method for solving genera...

We focus on robust and efficient iterative solvers for the pressure Poisson equation in incompressible Navier-Stokes problems. Preconditioned Krylov subspace methods are popular for these problems, with BiCGStab and GMRES(m) most frequently used for nonsymmetric systems. BiCGStab is popular because it has cheap iterations, but it may fail for stiff problems, especially early on as the initial g...

When powerful machines such as the Cray-2 became available in the late 1980s, a number of researchers investiWe investigate the use of an inexact Newton’s method to solve the potential equations in the transonic regime. As a test case, gated use of exact Newton’s method for solving steady we solve the two-dimensional steady transonic small disturbance state CFD problems. Direct sparse matrix so...

In large-scale scienti c computing, linear sparse solver is one of the most time-consuming process. In GeoFEM, various types of preconditioned iterative method is implemented on massively parallel computers. It has been well-known that ILU(0) factorization is very e ective preconditioning method for iterative solver. But it's also well-known that this method requires global data dependency and ...

There is a need for flexible iterative solvers that can solve large-scale (> 106 unknowns) nonsymmetric sparse linear systems to a small tolerance. Among flexible solvers, flexible GMRES (FGMRES) is attractive because it minimizes the residual norm over a particular subspace. In practice, FGMRES is often restarted periodically to keep memory and work requirements reasonable; however, like resta...

Convergence results are provided for inexact inverse subspace iteration applied to the problem of finding the invariant subspace associated with a small number of eigenvalues of a large sparse matrix. These results are illustrated by the use of block-GMRES as the iterative solver. The costs of the inexact solves are measured by the number of inner iterations needed by the iterative solver at ea...

Streamline upwind/Petrov–Galerkin formulation for convec-tion dominated flows with particular emphasis on the incompressible Navier–Stokes equations. A dynamic mesh partition algorithm for the finite element solution of two phase immiscible flow in oil reservoirs. Finite elements in fluids. K. Characteristic adaptive subdo-main methods for reservoir flow problems. Matrix–dependent pro-longation...

In tackling the problem of minimizing the deformation of a loaded structure, by varying the shape of the original structure, past second order optimization efforts have focused on general Newton techniques like the Davidon-Fletcher-Powell (DFP) update formula and the BroydenFletcher-Goldfarb-Shanno (BFGS) formula which iteratively build estimates of the structure's Hessian. This thesis bypasses...